Question: ${\sqrt[3]{500} = \text{?}}$
$\sqrt[3]{500}$ is the number that, when multiplied by itself three times, equals $500$ First break down $500$ into its prime factorization and look for factors that appear three times. So the prime factorization of $500$ is $2\times 2\times 5\times 5\times 5$ Notice that we can rearrange the factors like so: $500 = 2 \times 2 \times 5 \times 5 \times 5 = (5\times 5\times 5) \times 2\times 2$ So $\sqrt[3]{500} = \sqrt[3]{5\times 5\times 5} \times \sqrt[3]{2\times 2}$ $\sqrt[3]{500} = 5 \times \sqrt[3]{2\times 2}$ $\sqrt[3]{500} = 5 \sqrt[3]{4}$